9) Jon is playing a game. He starts with some points. On his first turn, Jon wins 6 points. On his second turn, Jon’s points are doubled. He then has 26 points. How many points did Jon start with?
Write an equation to model this problem.
Solve the equation.
Verify the solution.
(s + 6) * 2 = 26
To solve this problem, we will first set up an equation to represent the given information.
Let's assume Jon started with "x" points.
On his first turn, Jon wins 6 points, so his total points become x + 6.
On his second turn, his points are doubled, so his total points become 2(x + 6).
We also know that Jon's total points after the second turn is 26.
So, the equation representing this information is:
2(x + 6) = 26.
Now, we can solve this equation to find the value of x.
To do so, we'll simplify the equation by distributing the 2 on the left side:
2x + 12 = 26.
Next, we'll isolate the variable x by subtracting 12 from both sides:
2x = 26 - 12,
2x = 14.
Finally, to solve for x, we divide both sides of the equation by 2:
x = 14/2,
x = 7.
Therefore, Jon started with 7 points.
To verify if our solution is correct, we substitute the value of x into the original equation:
2(7 + 6) = 26,
2(13) = 26,
26 = 26.
Since the equation is true, our solution is correct, and Jon indeed started with 7 points.
To solve this problem, we need to set up an equation using the information given. Let's call the number of points Jon started with "x".
According to the problem, on Jon's first turn, he wins 6 points. So, after the first turn, he will have x + 6 points.
On his second turn, Jon's points are doubled. This means he will have 2 times the number of points he had after the first turn. Therefore, after the second turn, Jon will have 2(x + 6) points, which is equal to 26 points.
Now we can write the equation:
2(x + 6) = 26
To solve this equation, we will start by simplifying the left side:
2x + 12 = 26
Next, we will isolate the variable on one side of the equation by subtracting 12 from both sides:
2x = 26 - 12
2x = 14
Finally, we can solve for x by dividing both sides of the equation by 2:
x = 14 / 2
x = 7
Therefore, Jon started with 7 points.
To verify our solution, we can substitute the value of x back into the original equation:
2(7 + 6) = 26
Simplifying the left side:
2(13) = 26
26 = 26
Since both sides of the equation are equal, we can confirm that our solution is correct. Jon indeed started with 7 points.